Doing Bayesian data analysis a tutorial with R, JAGS, and Stan

Detalles Bibliográficos
Otros Autores:	Kruschke, John K., author (author)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Amsterdam : Academic Press is an imprint of Elsevier [2015]
Edición:	2nd ed
Materias:	Estadística bayesiana. R (Lenguaje de programación)
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628404206719

Tabla de Contenidos:

Front Cover
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan
Copyright
Dedication
Contents
Chapter 1: What's in This Book (Read This First!)
1.1 Real People Can Read This Book
1.1.1 Prerequisites
1.2 What's in This Book
1.2.1 You're busy. What's the least you can read?
1.2.2 You're really busy! Isn't there even less you can read?
1.2.3 You want to enjoy the view a little longer. But not too much longer
1.2.4 If you just gotta reject a null hypothesis…
1.2.5 Where's the equivalent of traditional test X in this book?
1.3 What's New in the Second Edition?
1.4 Gimme Feedback (Be Polite)
1.5 Thank You!
Part I: The Basics: Models, Probability, Bayes' Rule, and R
Chapter 2: Introduction: Credibility, Models, and Parameters
2.1 Bayesian Inference Is Reallocation of CredibilityAcross Possibilities
2.1.1 Data are noisy and inferences are probabilistic
2.2 Possibilities Are Parameter Values in Descriptive Models
2.3 The Steps of Bayesian Data Analysis
2.3.1 Data analysis without parametric models?
2.4 Exercises
Chapter 3: The R Programming Language
3.1 Get the Software
3.1.1 A look at RStudio
3.2 A Simple Example of R in Action
3.2.1 Get the programs used with this book
3.3 Basic Commands and Operators in R
3.3.1 Getting help in R
3.3.2 Arithmetic and logical operators
3.3.3 Assignment, relational operators, and tests of equality
3.4 Variable Types
3.4.1 Vector
3.4.1.1 The combine function
3.4.1.2 Component-by-component vector operations
3.4.1.3 The colon operator and sequence function
3.4.1.4 The replicate function
3.4.1.5 Getting at elements of a vector
3.4.2 Factor
3.4.3 Matrix and array
3.4.4 List and data frame
3.5 Loading and Saving Data
3.5.1 The read.csv and read.table functions.
3.5.2 Saving data from R
3.6 Some Utility Functions
3.7 Programming in R
3.7.1 Variable names in R
3.7.2 Running a program
3.7.3 Programming a function
3.7.4 Conditions and loops
3.7.5 Measuring processing time
3.7.6 Debugging
3.8 Graphical Plots: Opening and Saving
3.9 Conclusion
3.10 Exercises
Chapter 4: What Is This Stuff Called Probability?
4.1 The Set of All Possible Events
4.1.1 Coin flips: Why you should care
4.2 Probability: Outside or Inside the Head
4.2.1 Outside the head: Long-run relative frequency
4.2.1.1 Simulating a long-run relative frequency
4.2.1.2 Deriving a long-run relative frequency
4.2.2 Inside the head: Subjective belief
4.2.2.1 Calibrating a subjective belief by preferences
4.2.2.2 Describing a subjective belief mathematically
4.2.3 Probabilities assign numbers to possibilities
4.3 Probability Distributions
4.3.1 Discrete distributions: Probability mass
4.3.2 Continuous distributions: Rendezvous with density
4.3.2.1 Properties of probability density functions
4.3.2.2 The normal probability density function
4.3.3 Mean and variance of a distribution
4.3.3.1 Mean as minimized variance
4.3.4 Highest density interval (HDI)
4.4 Two-Way Distributions
4.4.1 Conditional probability
4.4.2 Independence of attributes
4.5 Appendix: R Code for Figure 4.1
4.6 Exercises
Chapter 5: Bayes' Rule
5.1 Bayes' Rule
5.1.1 Derived from definitions of conditional probability
5.1.2 Bayes' rule intuited from a two-way discrete table
5.2 Applied to Parameters and Data
5.2.1 Data-order invariance
5.3 Complete Examples: Estimating Bias in a Coin
5.3.1 Influence of sample size on the posterior
5.3.2 Influence of the prior on the posterior
5.4 Why Bayesian Inference Can Be Difficult.
5.5 Appendix: R Code for Figures 5.1, 5.2, etc.
5.6 Exercises
Part II: All the Fundamentals Applied to Inferring a Binomial Probability
Chapter 6: Inferring a Binomial Probability via Exact Mathematical Analysis
6.1 The Likelihood Function: Bernoulli Distribution
6.2 A Description of Credibilities: The Beta Distribution
6.2.1 Specifying a beta prior
6.3 The Posterior Beta
6.3.1 Posterior is compromise of prior and likelihood
6.4 Examples
6.4.1 Prior knowledge expressed as a beta distribution
6.4.2 Prior knowledge that cannot be expressed as a beta distribution
6.5 Summary
6.6 Appendix: R Code for Figure 6.4
6.7 Exercises
Chapter 7: Markov Chain Monte Carlo
7.1 Approximating a Distribution with a Large Sample
7.2 A Simple Case of the Metropolis Algorithm
7.2.1 A politician stumbles upon the Metropolis algorithm
7.2.2 A random walk
7.2.3 General properties of a random walk
7.2.4 Why we care
7.2.5 Why it works
7.3 The Metropolis Algorithm More Generally
7.3.1 Metropolis algorithm applied to Bernoulli likelihood and beta prior
7.3.2 Summary of Metropolis algorithm
7.4 Toward Gibbs Sampling: Estimating Two Coin Biases
7.4.1 Prior, likelihood and posterior for two biases
7.4.2 The posterior via exact formal analysis
7.4.3 The posterior via the Metropolis algorithm
7.4.4 Gibbs sampling
7.4.5 Is there a difference between biases?
7.4.6 Terminology: MCMC
7.5 MCMC Representativeness, Accuracy, and Efficiency
7.5.1 MCMC representativeness
7.5.2 MCMC accuracy
7.5.3 MCMC efficiency
7.6 Summary
7.7 Exercises
Chapter 8: JAGS
8.1 JAGS and its Relation to R
8.2 A Complete Example
8.2.1 Load data
8.2.2 Specify model
8.2.3 Initialize chains
8.2.4 Generate chains
8.2.5 Examine chains
8.2.5.1 The plotPost function.
8.3 Simplified Scripts for Frequently Used Analyses
8.4 Example: Difference of Biases
8.5 Sampling from the Prior Distribution in JAGS
8.6 Probability Distributions Available in JAGS
8.6.1 Defining new likelihood functions
8.7 Faster Sampling with Parallel Processing in RunJAGS
8.8 Tips for Expanding JAGS Models
8.9 Exercises
Chapter 9: Hierarchical Models
9.1 A Single Coin from a Single Mint
9.1.1 Posterior via grid approximation
9.2 Multiple Coins from a Single Mint
9.2.1 Posterior via grid approximation
9.2.2 A realistic model with MCMC
9.2.3 Doing it with JAGS
9.2.4 Example: Therapeutic touch
9.3 Shrinkage in Hierarchical Models
9.4 Speeding up JAGS
9.5 Extending the Hierarchy: Subjects Within Categories
9.5.1 Example: Baseball batting abilities by position
9.6 Exercises
Chapter 10: Model Comparison and Hierarchical Modeling
10.1 General Formula and the Bayes Factor
10.2 Example: Two Factories of Coins
10.2.1 Solution by formal analysis
10.2.2 Solution by grid approximation
10.3 Solution by MCMC
10.3.1 Nonhierarchical MCMC computation of each model'smarginal likelihood
10.3.1.1 Implementation with JAGS
10.3.2 Hierarchical MCMC computation of relative model probability
10.3.2.1 Using pseudo-priors to reduce autocorrelation
10.3.3 Models with different "noise" distributions in JAGS
10.4 Prediction: Model Averaging
10.5 Model Complexity Naturally Accounted for
10.5.1 Caveats regarding nested model comparison
10.6 Extreme Sensitivity to Prior Distribution
10.6.1 Priors of different models should be equally informed
10.7 Exercises
Chapter 11: Null Hypothesis Significance Testing
11.1 Paved with Good Intentions
11.1.1 Definition of p value
11.1.2 With intention to fix N
11.1.3 With intention to fix z.
11.1.4 With intention to fix duration
11.1.5 With intention to make multiple tests
11.1.6 Soul searching
11.1.7 Bayesian analysis
11.2 Prior Knowledge
11.2.1 NHST analysis
11.2.2 Bayesian analysis
11.2.2.1 Priors are overt and relevant
11.3 Confidence Interval and Highest Density Interval
11.3.1 CI depends on intention
11.3.1.1 CI is not a distribution
11.3.2 Bayesian HDI
11.4 Multiple Comparisons
11.4.1 NHST correction for experimentwise error
11.4.2 Just one Bayesian posterior no matter how you look at it
11.4.3 How Bayesian analysis mitigates false alarms
11.5 What a Sampling Distribution Is Good For
11.5.1 Planning an experiment
11.5.2 Exploring model predictions (posterior predictive check)
11.6 Exercises
Chapter 12: Bayesian Approaches to Testing a Point ("Null") Hypothesis
12.1 The Estimation Approach
12.1.1 Region of practical equivalence
12.1.2 Some examples
12.1.2.1 Differences of correlated parameters
12.1.2.2 Why HDI and not equal-tailed interval?
12.2 The Model-Comparison Approach
12.2.1 Is a coin fair or not?
12.2.1.1 Bayes' factor can accept null with poor precision
12.2.2 Are different groups equal or not?
12.2.2.1 Model specification in JAGS
12.3 Relations of Parameter Estimation and Model Comparison
12.4 Estimation or Model Comparison?
12.5 Exercises
Chapter 13: Goals, Power, and Sample Size
13.1 The Will to Power
13.1.1 Goals and obstacles
13.1.2 Power
13.1.3 Sample size
13.1.4 Other expressions of goals
13.2 Computing Power and Sample Size
13.2.1 When the goal is to exclude a null value
13.2.2 Formal solution and implementation in R
13.2.3 When the goal is precision
13.2.4 Monte Carlo approximation of power
13.2.5 Power from idealized or actual data.
13.3 Sequential Testing and the Goal of Precision.

Doing Bayesian data analysis a tutorial with R, JAGS, and Stan

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